Cosmological Correlators in Gauge Theory and Gravity from EAdS

In this work we examine in more detail the map between late-time correlators in de Sitter space and boundary correlators in Euclidean anti-de Sitter space, elaborating on the general construction presented in arXiv:2007.09993 and arXiv:2109.02725 for EFTs of bosonic spinning fields. This map may be phrased as an equivalence between the generating functional of late-time correlators in the Schwinger-Keldysh formalism and the generating functional for boundary correlators in the corresponding EAdS theory. We extend the construction to gauge bosons and gravitons, and clarify additional subtleties that appear in even boundary dimensions. Finally, we emphasise that the relation between dS and EAdS propagators is manifest in Mellin space, and we provide new expressions for gauge-boson and graviton propagators. These results provide a streamlined framework for the study of cosmological correlators involving spinning fields.

💡 Research Summary

The paper develops a systematic framework that maps late‑time cosmological correlators of gauge bosons and gravitons in de Sitter (dS) space to boundary correlators of a Euclidean Anti‑de Sitter (EAdS) theory. Building on earlier work that treated scalar and integer‑spin fields, the authors extend the construction to massless spin‑1 and spin‑2 fields, which are central to inflationary physics.

The starting point is the Schwinger‑Keldysh (in‑in) formalism, where four bulk‑to‑bulk propagators (G^{\pm\pm}) appear. By choosing the Bunch‑Davies vacuum and implementing an (i\epsilon) prescription, the contour in the complex conformal‑time plane is rotated 90° for each branch: (z_{+}=+i(-\eta)) and (z_{-}=-i(-\eta)). This “double Wick rotation” maps the dS propagators to linear combinations of EAdS bulk‑to‑bulk propagators with scaling dimensions (\Delta_{\pm}=d/2\pm i\nu). The relation is made explicit in equation (2.14), where each dS propagator is expressed as a sum of two EAdS propagators weighted by phase factors (\exp